Question

The diagonal of a rectangle is 60 m more than its shorter side and the larger side is 30 m more than the shorter side. Find the sides of the rectangle.

Answer 1

Let the shorter side be x m.
Length of the other side = (x + 30) m
Length of hypotenuse = (x + 60) m
Using Pythagoras theorem,
$(x+60{)}^2=x^2+(x+30{)}^2$
$x^2+3600+120x=x^2+x^2+900+60x$
$x^2–60x–2700=0$
$x^2–90x+30x–2700=0$
$x(x–90)+30(x–90)=0$
$(x–90)(x+30)=0$
x = 90, -30
But, x cannot be negative. So, x = 90.
Thus, the sides of the rectangle are 90 m and (90 + 30) m = 120 m.